Abstract
Second-order sufficient optimality conditions (SSC) are derived for an optimal control problem subject to mixed control-state and pure state constraints of order one. The proof is based on a Hamilton-Jacobi inequality and it exploits the regularity of the control function as well as the associated Lagrange multipliers. The obtained SSC involve the strict Legendre-Clebsch condition and the solvability of an auxiliary Riccati equation. They are weakened by taking into account the strongly active constraints.
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Malanowski, K., Maurer, H. & Pickenhain, S. Second-Order Sufficient Conditions for State-Constrained Optimal Control Problems. Journal of Optimization Theory and Applications 123, 595–617 (2004). https://doi.org/10.1007/s10957-004-5725-0
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DOI: https://doi.org/10.1007/s10957-004-5725-0